Conservation of Momentum of cannonballs

[okgo]

Homework Statement

You are shooting cannonballs from a cannon. To achieve the maximum range of the ball, would you be better off fastening the cannon to the ground or letting it be free to recoil, or wouldn't it matter? Explain your reasoning

Homework Equations

Conservation of momentum

The Attempt at a Solution

Like in a gun, there is a recoil, but since the gun has a larger mass than the bullet, its velocity is less.

But I don't think it would matter if the cannon was fasten to the ground because wouldn't the recoil of the cannon would be transferred to the bolts and ground, therefore the cannonball would still fire at maximum range?

 

[LowlyPion]

Homework Statement

You are shooting cannonballs from a cannon. To achieve the maximum range of the ball, would you be better off fastening the cannon to the ground or letting it be free to recoil, or wouldn't it matter? Explain your reasoning

Homework Equations

Conservation of momentum

The Attempt at a Solution

Like in a gun, there is a recoil, but since the gun has a larger mass than the bullet, its velocity is less.

But I don't think it would matter if the cannon was fasten to the ground because wouldn't the recoil of the cannon would be transferred to the bolts and ground, therefore the cannonball would still fire at maximum range?

Consider 2 cases. One you have 2 blocks in space with a spring that pops them in opposite directions. In that case from Newton's Third Law won't each get half the energy as each pushes against the other equally? The center of mass stays the same. The second case is a block pushed by a spring from against a wall. Same PE in the spring. Which gets more kinetic energy?

 

[nlightner]

Your reasoning is correct. The conservation of momentum states that the total momentum of a system remains constant. In this case, the system includes both the cannon and the cannonball. Whether the cannon is fastened to the ground or allowed to recoil will not affect the momentum of the system. The momentum of the cannon will be transferred to the cannonball, resulting in the same range regardless of the cannon's movement. However, it is important to consider the safety of the cannon operator. If the cannon is not fastened to the ground, it may recoil and potentially cause harm to the operator. Therefore, it is recommended to fasten the cannon to the ground for safety reasons.